For a function analytic in a compact domain and continuous in its closure, it is shown that the modules of continuity on the boundary of the domain and in its closure coincide.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 8, pp. 1106–1113, August, 2010.
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Trokhimchuk, Y.Y. Modules of continuity and analytic functions. Ukr Math J 62, 1285–1294 (2011). https://doi.org/10.1007/s11253-011-0429-8
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DOI: https://doi.org/10.1007/s11253-011-0429-8